Bottom Line:
Although calcium homeostasis emerged efficaciously across all models in the population, disparate changes in ionic conductances that mediated this emergence resulted in variable plasticity to several intrinsic properties, also manifesting as significant differences in firing responses across models.We found that the conductance values, intrinsic properties, and firing response of neurons exhibited differential robustness to an intervening switch in the type of afferent activity.These results unveil critical dissociations between different forms of homeostasis, and call for a systematic evaluation of the impact of state-dependent switches in afferent activity on neuronal intrinsic properties during neural coding and homeostasis.

ABSTRACTHow do neurons reconcile the maintenance of calcium homeostasis with perpetual switches in patterns of afferent activity? Here, we assessed state-dependent evolution of calcium homeostasis in a population of hippocampal pyramidal neuron models, through an adaptation of a recent study on stomatogastric ganglion neurons. Calcium homeostasis was set to emerge through cell-autonomous updates to 12 ionic conductances, responding to different types of synaptically driven afferent activity. We first assessed the impact of theta-frequency inputs on the evolution of ionic conductances toward maintenance of calcium homeostasis. Although calcium homeostasis emerged efficaciously across all models in the population, disparate changes in ionic conductances that mediated this emergence resulted in variable plasticity to several intrinsic properties, also manifesting as significant differences in firing responses across models. Assessing the sensitivity of this form of plasticity, we noted that intrinsic neuronal properties and the firing response were sensitive to the target calcium concentration and to the strength and frequency of afferent activity. Next, we studied the evolution of calcium homeostasis when afferent activity was switched, in different temporal sequences, between two behaviorally distinct types of activity: theta-frequency inputs and sharp-wave ripples riding on largely silent periods. We found that the conductance values, intrinsic properties, and firing response of neurons exhibited differential robustness to an intervening switch in the type of afferent activity. These results unveil critical dissociations between different forms of homeostasis, and call for a systematic evaluation of the impact of state-dependent switches in afferent activity on neuronal intrinsic properties during neural coding and homeostasis.

Figure 3: Evolution of ionic conductances and intrinsic measurements through cell-autonomous self-regulation of calcium homeostasis in model neurons receiving theta-frequency inputs. A, Temporal evolution of the internal calcium concentration (left), the 12 ionic conductances in the model (Leak, NaF, KDR, KA, KM, HCN, CaL, CaN, CaR, CaT, BK, SK; middle) and membrane voltage (right) in a model neuron receiving sinusoidal input of 8 Hz. The firing pattern of the neuron is shown at the three different temporal locations (middle). B, Firing pattern of four different model neurons at steady-state of theta-dependent evolution. All traces are for a 1 s period. C, Histogram of gNa measured at steady state of evolution with θ-frequency oscillations (black). Also plotted is the histogram of base values of gNa obtained from GSA. Histograms are across the 78 valid models. D, Top, Seven intrinsic measurements (f250, VAP, Rin, /Z/max, fR, Q, ΦL) at steady state of theta-dependent evolution (θ) of six different valid models (color-coded) compared with the corresponding baseline GSA values (GSA). Bottom, Histograms of the percentage change in the seven measurements at steady state of theta-dependent evolution from the corresponding baseline GSA values, plotted for all 78 valid models. Percentage change in subthreshold measurements (Rin, /Z/max, fR, Q, ΦL) were computed only for those models that did not fire action potentials in response to the injected stimulus. In addition, models that showed very high percentage changes in ΦL were eliminated. The number of models (n) used for each histogram is mentioned in the respective panel.

Mentions:
We set the time constants () for the evolution of mRNAs with reference to each channel from the corresponding conductances obtained from the valid model (Eq. 23), and implemented the evolution of calcium homeostasis (Eqs. 21, 22) for each of the 78 valid models. The neurons were presented with theta-frequency afferent activity, modeled as an 8 Hz sinusoidal permeability change in synaptic receptors. The mRNAs and conductances were allowed to evolve in time until a steady state was achieved in the cytosolic calcium concentration and the conductance values (Fig. 3A). During the initial phase of the evolution process, the voltage response of the model neuron to the sinusoidal input conductance corresponded to large-amplitude oscillations with small action potential amplitudes (Fig. 3A). We noted that this was consequent to the initial low values of all conductances, implying a large input resistance leading to large-amplitude voltage oscillations. The small action potential amplitudes, on the other hand, were consequent to the lower values of the spike-generating fast sodium conductance. As the calcium-dependent evolution progressed toward achieving the target calcium value, the voltage response corresponded to large-amplitude action potentials within each theta cycle (Fig. 3A).

Figure 3: Evolution of ionic conductances and intrinsic measurements through cell-autonomous self-regulation of calcium homeostasis in model neurons receiving theta-frequency inputs. A, Temporal evolution of the internal calcium concentration (left), the 12 ionic conductances in the model (Leak, NaF, KDR, KA, KM, HCN, CaL, CaN, CaR, CaT, BK, SK; middle) and membrane voltage (right) in a model neuron receiving sinusoidal input of 8 Hz. The firing pattern of the neuron is shown at the three different temporal locations (middle). B, Firing pattern of four different model neurons at steady-state of theta-dependent evolution. All traces are for a 1 s period. C, Histogram of gNa measured at steady state of evolution with θ-frequency oscillations (black). Also plotted is the histogram of base values of gNa obtained from GSA. Histograms are across the 78 valid models. D, Top, Seven intrinsic measurements (f250, VAP, Rin, /Z/max, fR, Q, ΦL) at steady state of theta-dependent evolution (θ) of six different valid models (color-coded) compared with the corresponding baseline GSA values (GSA). Bottom, Histograms of the percentage change in the seven measurements at steady state of theta-dependent evolution from the corresponding baseline GSA values, plotted for all 78 valid models. Percentage change in subthreshold measurements (Rin, /Z/max, fR, Q, ΦL) were computed only for those models that did not fire action potentials in response to the injected stimulus. In addition, models that showed very high percentage changes in ΦL were eliminated. The number of models (n) used for each histogram is mentioned in the respective panel.

Mentions:
We set the time constants () for the evolution of mRNAs with reference to each channel from the corresponding conductances obtained from the valid model (Eq. 23), and implemented the evolution of calcium homeostasis (Eqs. 21, 22) for each of the 78 valid models. The neurons were presented with theta-frequency afferent activity, modeled as an 8 Hz sinusoidal permeability change in synaptic receptors. The mRNAs and conductances were allowed to evolve in time until a steady state was achieved in the cytosolic calcium concentration and the conductance values (Fig. 3A). During the initial phase of the evolution process, the voltage response of the model neuron to the sinusoidal input conductance corresponded to large-amplitude oscillations with small action potential amplitudes (Fig. 3A). We noted that this was consequent to the initial low values of all conductances, implying a large input resistance leading to large-amplitude voltage oscillations. The small action potential amplitudes, on the other hand, were consequent to the lower values of the spike-generating fast sodium conductance. As the calcium-dependent evolution progressed toward achieving the target calcium value, the voltage response corresponded to large-amplitude action potentials within each theta cycle (Fig. 3A).

Bottom Line:
Although calcium homeostasis emerged efficaciously across all models in the population, disparate changes in ionic conductances that mediated this emergence resulted in variable plasticity to several intrinsic properties, also manifesting as significant differences in firing responses across models.We found that the conductance values, intrinsic properties, and firing response of neurons exhibited differential robustness to an intervening switch in the type of afferent activity.These results unveil critical dissociations between different forms of homeostasis, and call for a systematic evaluation of the impact of state-dependent switches in afferent activity on neuronal intrinsic properties during neural coding and homeostasis.

ABSTRACTHow do neurons reconcile the maintenance of calcium homeostasis with perpetual switches in patterns of afferent activity? Here, we assessed state-dependent evolution of calcium homeostasis in a population of hippocampal pyramidal neuron models, through an adaptation of a recent study on stomatogastric ganglion neurons. Calcium homeostasis was set to emerge through cell-autonomous updates to 12 ionic conductances, responding to different types of synaptically driven afferent activity. We first assessed the impact of theta-frequency inputs on the evolution of ionic conductances toward maintenance of calcium homeostasis. Although calcium homeostasis emerged efficaciously across all models in the population, disparate changes in ionic conductances that mediated this emergence resulted in variable plasticity to several intrinsic properties, also manifesting as significant differences in firing responses across models. Assessing the sensitivity of this form of plasticity, we noted that intrinsic neuronal properties and the firing response were sensitive to the target calcium concentration and to the strength and frequency of afferent activity. Next, we studied the evolution of calcium homeostasis when afferent activity was switched, in different temporal sequences, between two behaviorally distinct types of activity: theta-frequency inputs and sharp-wave ripples riding on largely silent periods. We found that the conductance values, intrinsic properties, and firing response of neurons exhibited differential robustness to an intervening switch in the type of afferent activity. These results unveil critical dissociations between different forms of homeostasis, and call for a systematic evaluation of the impact of state-dependent switches in afferent activity on neuronal intrinsic properties during neural coding and homeostasis.